Uniformly Weighted Moving Average (UWMA) chart
A uniformly weighted moving average (UWMA) chart is a type of control chart used to monitor small shifts in the process mean. It uses the average of a number of consecutive observations.
The UWMA chart plots the moving average for individual measurements or subgroup means.
Given a series of observations and a fixed subset size, the first element of the moving average is the average of the initial subset of the number series. Then the subset is modified by "shifting forward"; that is, excluding the first number of the series and including the next number following the subset in the series. The next element of the moving average is the average of this subset. This process is repeated over the entire series creating the moving average statistic.
- A fixed subset size, the number of successive observations (span) in the moving average. Span must satisfy 1 < span ≤ n. Default span=3.
A small span reduces the influence of older observations; a large span slows the response to large shifts. In general, the magnitude of the shift to detect and the span are inversely related.
Each point on the chart represents the value of a moving average.
The center line is the process mean. If unspecified, the process mean is the weighted mean of the subgroup means or the mean of the individual observations.
The control limits are a multiple (L) of sigma above and below the center line. Default L=3. If unspecified, the process sigma is the pooled standard deviation of the subgroups, or the standard deviation of the individual observations, unless the chart is combined with an R-, S-, or MR- chart where it is estimated as described for the respective chart.
UWMA is sensitive to small shifts in the process mean, but is not as effective as either the CUSUM or EWMA (Montgomery 2012).
